How would I create a stripe on top of a brick texture?
Use two brick textures. The trick is thinking of one that can be used as a mask to mix the original texture with some other color, the white elements will be one texture, the black elements will be a color (or a different texture if plugged to the other socket of a mix color node).

On the second brick texture play with scale Mortar size and Brick, until you get a black and white pattern. This pattern (or mask) will be used to determine what parts of the object get the small bricks.
Evaluate the results by plugging the output to the shader you will use, but using the Fac output instead of color.

Then use that same Fac output to control the color on a color mix node.

Additionally, you can use a mapping node to set the texture's scale on $X$ to zero so that you are left only with horizontal stripes.